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Optimal oral drug dosing via application of the contraction mapping theorem

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Evans, N. D.. (2011) Optimal oral drug dosing via application of the contraction mapping theorem. Biomedical Signal Processing and Control, Vol.6 (No.1). pp. 57-63. ISSN 1746-8094

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Official URL: http://dx.doi.org/10.1016/j.bspc.2010.06.006

Abstract

The problem of determining an oral dose, or schedule of oral doses, that gives rise to an arbitrary area-under-curve or to points on the time-series for a variable of interest in a drug kinetics model is considered. These two measures are considered as surrogates for the particular drug response to the dose. The approach taken is to formulate the problem as a fixed point one to which a version of the contraction mapping theorem can be applied. The results, illustrated for a model for the anti-cancer agent topotecan, demonstrate the applicability of the approach.

Item Type:	Journal Article
Subjects:	R Medicine > RM Therapeutics. Pharmacology T Technology > TA Engineering (General). Civil engineering (General)
Divisions:	Faculty of Science > Engineering
Library of Congress Subject Headings (LCSH):	Pharmacokinetics -- Mathematical models
Journal or Publication Title:	Biomedical Signal Processing and Control
Publisher:	Elsevier BV
ISSN:	1746-8094
Date:	January 2011
Volume:	Vol.6
Number:	No.1
Page Range:	pp. 57-63
Identification Number:	10.1016/j.bspc.2010.06.006
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Description:	Biomedical signal processing (Extended selected papers from the 7th IFAC Symposium on Modelling and Control in Biomedical Systems(MCBMS'09))
Version or Related Resource:	This item was originally submitted to the 7th IFAC Symposium on Modelling and Control in Biomedical Systems, Aalborg, Denmark, Aug 12 - 14, 2009.
References:	[1] N. D. Evans, R. J. Errington, M. J. Chapman, P. J. Smith, M. J. Chap pell, K. R. Godfrey, Compartmental modelling of the uptake kinetics of the anti-cancer agent topotecan in human breast cancer cells, Inter national Journal of Adaptive Control and Signal Processing 19 (2005) 395–417. [2] J. O’Leary, F.M.Muggia, Camptothecins: a review of their development and schedules of administration, European Journal of Cancer 34 (1998) 1500–1508. [3] Y. H. Hsiang, L. F. Lui, Identification of mammalian DNA topoisomerase-I as an intracellular target of the anticancer drug camp tothecin, Cancer Research 48 (1988) 1722–1726. [4] C. Bailly, Topoisomerase I poisons and suppressors as anticancer drugs, Current Medicinal Chemistry 7 (2000) 39–58. [5] M. J. Chappell, N. D. Evans, R. J. Errington, I. A. Khan, L. Camp bell, R. Ali, K. R. Godfrey, P. J. Smith, A coupled drug kinetics-cell cycle model to analyse the response of human cells to intervention by topotecan, Computer Methods and Programs in Biomedicine 89 (2008) 169–178. [6] N. D. Evans, A. J. Pritchard, A control theoretic approach to containing the spread of rabies, IMA Journal of Mathematics Applied in Medicine and Biology 18 (2001) 1–23. [7] H. Hermes, Controllability and the singular problem, Journal of the Society for Industrial and Applied Mathematics, Series A: Control 2 (1964) 241–260. [8] E. J. Davison, E. C. Kunze, Some sufficient conditions for the global and local controllability of nonlinear time varying systems, SIAM Journal on Control 8 (1970) 489–497. [9] K. Magnusson, A. J. Pritchard, Local exact controllability of nonlinear evolution equations, in: R. Conti (Ed.), Recent advances in differential equations, Academic Press, London, 271–280, 1981. [10] N. Carmichael, M. D. Quinn, Fixed-point methods in nonlinear control, IMA Journal of Mathematical Control and Information 5 (1988) 41–67. [11] L. Collatz, Functional analysis and numerical mathematics, Academic Press, New York, 1966.
URI:	http://wrap.warwick.ac.uk/id/eprint/37150